Vela was born in Harlingen, Texas and raised in Brownsville, Texas. His father, Filemon Bartolome Vela Sr., was a long-serving United States federal judge. The Reynaldo G. Garza-Filemon B. Vela United States Courthouse in Brownsville is named in Judge Vela's honor. His mother, Blanca Sanchez Vela, served as Brownsville's first female mayor from 1999 to 2003.